During the titration of $0.1 \, M$ $CH_3COOH$ and $0.1 \, M$ $KOH$ solution,what will be the $pH$ of the solution after $40\%$ neutralization of the acid? [$K_a$ for $CH_3COOH = 2 \times 10^{-5}$]

Six wires each of cross-sectional area $A$ and length $l$ are combined as shown in the figure. The thermal conductivities of copper and iron are $K_1$ and $K_2$ respectively. The equivalent thermal resistance between points $A$ and $C$ is

Find the values of $x$,if: $(i)$ $\left|\begin{array}{ll}2 & 4 \\ 5 & 1\end{array}\right|=\left|\begin{array}{cc}2 x & 4 \\ 6 & x\end{array}\right|$ (ii) $\left|\begin{array}{ll}2 & 3 \\ 4 & 5\end{array}\right|=\left|\begin{array}{ll}x & 3 \\ 2 x & 5\end{array}\right|$

The resolving limit of a healthy human eye is about

$Cl_2 + \mathop{NaOH}\limits_{(\text{dil and cold})} \longrightarrow A + B + H_2O$. The anions of $A$ and $B$ are respectively . . . . . . .

If the number of diagonals of a regular polygon is $35$,then the number of sides of the polygon is